Hey, I almost never read this board as it is the land of live in maids, water features, petty gripes and 5k-10k a month expense packages.
Anyways, I am one of the rare (but increasingly more common) expats living on local wages.
To answer your question, $2k is going to be tight. Lots of properties are in the $5k range. That being said, we pay only a tiny bit more then that for our tiny studio (nicely furnished.) But, we arrived with small suitcases and wanted to get a feel for the areas without much commitment to furniture.
We turned down an amazing, huge 2 bedroom unfurnished
condo right near Kandahar for $2150 with an incredible view of the top of the Mosque.
On the other end, you can find a renovated 2 bedroom HDB for several hundred less then your budget (or more in the heartlands.)
Much will depend on what you want in terms of a neighborhood. We love living in little India as it fits our lifestyle much more then any of the typical expat enclaves. We actually had to twist the arm of our realtors to have them show us anything AWAY from orchard road for instance. Singapore is like nowhere we had ever lived before - and we are very worldly. Our initial radar and considerations were admittedly far off the mark of our opinions now.
Take an easy $300 off any advertised price in this economic climate and be prepared to bargain hard. Also, we stayed in a cheap hotel (off lor 10, geylang... most who read this will get a chuckle) for the first month to really understand the areas and markets BUT we wish we stayed for a second just to give us time to look.
Also, you may be coming from an economy where the other numbers in your budget might go -down- once you get here. Mass transit and food were both expenses we sorely overestimated. Housing here, in general, seems to be a larger percentage expense then what we spent, but that isn't always a bad thing.
I live in the neighborhood near where you are considering an am approximately in your budget, so PM me if you have any questions.
Good luck!